Answer
Do nothing special. Abandon fear and apprehension. We must always take the Lord's Name. Continue doing so today as well, just as before.
Such apprehension-based injunctions have been established by certain shastras. They seek to keep you perpetually anxious and fearful.
Any dharma or religion that instills fear of anything other than one's own sinful actions is a dharma or religion worth abandoning. Devotees who have surrendered to the Lord are not frightened by planets and stars — not even by the cosmic dissolution (pralaya). Neither Shani, Rahu, Ketu, nor anyone else can cause them any harm.
Consider that the Lord, in the very beginning of Chapter 16 of the Gita, has spoken three verses describing the daivi sampada (divine qualities). The foremost among them is "abhaya" (fearlessness).
Therefore, eat, drink, live at ease, and forget about the eclipse. If complete sharanagati (surrender) has been attained, nothing needs to be done. If a partial sense of surrender has developed, continue chanting the Lord's Name — not out of fear, but for the sake of joy.
Today is Sunday, there is time — so let the devotees go to Vaikuntha and revel in the divine lilas of Hari. Let the devotees of Krishna sport with the Lord in Goloka, a division of Vaikuntha itself. Let the devotees of Shri Rama go to Saketa, another division of Vaikuntha, and rest at the feet of Bhagavan Rama and Bhagavati Sita, who are verily forms of Shri Vishnu.
All these realms are far above the sun and the moon — even the light of the sun does not reach there. Always remember this shloka:
Ananyashchintayanto mam ye janah paryupasate | Tesham nityabhiyuktanam yoga-kshemam vahamyaham |
The Lord Himself bears the yoga-kshema (welfare and protection) of the ananya bhakta (exclusive devotee). Why should such exclusive devotees worry about the positions of planets and stars?